Mathematical problems are alive-abstract concepts are concretized, scenes are created and perception is emphasized.
In mathematics teaching, starting from students' life experience and existing life background, we should talk about mathematics in connection with life, turn abstract mathematical concepts, theorems, formulas and laws into a series of interesting and rich life examples that students are familiar with, and provide students with a lot of perceptual materials, so that students can gradually understand abstract mathematical concepts, theorems and thinking methods from their initial perception, and at the same time let students know the background and development process of mathematical knowledge.
In recent years, with the deepening of mathematics reform, many teachers pay attention to providing one or two practical backgrounds when introducing new knowledge, so that students can understand that mathematics comes from life. However, this alone cannot guarantee students' awareness of application. Perhaps without the practical background provided by the teacher, it is difficult for students to find other practical backgrounds in their minds, and they will still regard what they have learned and real life as two independent systems, and they will not feel the application value of new knowledge, which gives us a profound lesson.
Mathematicization of life problems-the abstraction of practical problems, focusing on modeling.
For the new curriculum, the most important thing is to let students really understand mathematics. In this sense, mathematical modeling and mathematical application have proved to be very successful. As we all know, mathematics has a wide range of applications, which is one of the basic characteristics of mathematics. The continuous development of production and science and technology provides a broad prospect for the application of mathematics. The application status of mathematics is improving day by day, and mathematical modeling is becoming a major topic for mathematical and scientific workers.
The so-called mathematical model is a mathematical structure expressed in a generalized or approximate way in a formal mathematical language according to or referring to the characteristics or quantitative relations of things. All mathematical concepts, theories, formulas and equations in a broad sense (algebraic equation, functional equation, differential equation, integral equation, etc. ) and an algorithm system consisting of a series of formulas can be called a mathematical model.
The mathematical modeling process can be roughly illustrated by the following block diagram:
For example, the problem of changing beer: Xiaoming's father bought 10 bottles of beer from the store, and the store stipulated that three empty bottles could be exchanged for one bottle of beer. How many bottles of beer can Xiaoming drink if his father stops giving money?
The solution is: after drinking 10 bottle, you can exchange it for three bottles; After drinking, there are four empty bottles left, and then change one bottle. After drinking, there are two empty bottles left. At this time, you can borrow 1 empty bottle, and then you can change 1 empty bottle. You can drink 15 bottles in total. In this process, "borrowing a bottle" can be described as a coincidence.
Mathematics comes from life and must return to life. Mathematics can only be endowed with vitality and spirituality in life. The content of mathematics learning is far from life, which is undoubtedly the root cause of students' lack of interest in mathematics, making the original lively mathematics learning activities become lifeless. In view of this, mathematics teaching should be full of life breath, pay attention to real experience, and change the traditional "learning mathematics from books" into "learning mathematics from life".